Nuclear Annuli

Abramowitz M. Stegun 1., 1972. Handbook of Mathematical Functions. Dover Publ. N.Y. Carslaw H.S. Jaeger J.C. 1965. Conduction of Heat in Solids. Oxford Sc. Publ., Oxford. Claesson J. 2003. Drying and Resaturation of a Bentonite Annulus. An Analytical Solution. Report, Building Physics, Chalmers, Sweden. Rutqvist J., Noorishad J. Tsang C-F. 1999. Coupled Termohydromechanical Analysis of a Heater Test in Unsaturated Clay and Fractured Rock at the Kamaishi Mine. SKI report 99 50, the Swedish Nuclear Power Inspectorate. 

The upper hemisphere of the steel shell is surrounded by a shielding made of reinforced concrete with a wall thickness of about 2 m. This shielding protects the nuclear part of the plant against any external impact (e. g. gas explosion, military aircraft crash) it also significantly reduces the likelihood that radionuclides will escape to the environment. The interspace between the steel shell and the secondary containment is held at sub-atmospheric pressure, so that any radionuclides penetrating the steel shell via leaks in the event of a loss-of-coolant accident would be transported by the annulus air extraction system to the standby filters and retained here, thus preventing release to the environment. 

The structures of CD host-guest complexes determined by X-ray crystallography show the guest to reside either completely or partially within the CD annuli. However, the structure in the solid state is not necessarily identical to that in solution in which most CD studies have been conducted using a range of spectroscopic and other techniques. Nuclear magnetic resonance (NMR) provides the most direct evidence of complexation within the CD annulus... 

These results can only be rationalized by considering an electron as a flexible wave packet, rather than a point particle. In particular, as shown in Table 2, the volume of a given annular shell is reduced as the nuclear charge increases, which means that an electronic unit is compressed into less space. However, the effective dimensionless electronic radius of r/a remains constant as a decreases and defines the fine-structure constant as a = Jr/a. The dimensionless volume of the two-electron (15) annulus therefore remains constant and so does the effective separation of electrons in units of a. 

Further interesting is azacalix[4]arene 13b with a 1,3-alternate conformation, which has been demonstrated to be inflexible in solution [33]. Conformational behavior of 13b in solution was examined by means of relaxation time measurements (Fig. 10). A much smaller longitudinal relaxation time of 1.03 s was observed for the aromatic protons of 13b, as compared with 2.51 s reported for conformationally flexible p-fert-butylthiacalix[4]arene [34], demonstrating that the 1,3-conformation of 13b was inflexible in solution. This result was further supported by two additional experimental facts. First, NMR spectra of 13b were temperature independent [22, 33]. Second, the observed nuclear Overhauser effects were properly explained by considering a sole contribution of an inflexible 1,3-conformation of 13b [22]. X-ray crystallographic analysis revealed that a small annulus of 13b was responsible for the conformational immobilization by the small, but yet sufficiently bulky 0-methyl groups [33], which were too small for carbon-bridged calix[4]arenes to keep their conformations in solution [1,3,35,36]. 

H. Kim, H. Y. Kim, et al., Heat Transfer to Supercritical Pressure Carbon Dioxide Flowing Upward Through Tubes and a Narrow Annulus Passage, Progress in Nuclear Energy, Vol. 50, 518-525 (2008)... 

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