Rotation bodily

The reaction tank (Figure 11.14) is constructed of rubber-coated steel or concrete and is lined with carbon bricks. Baffles are fitted onto the walls to prevent the slurry from rotating bodily as a single mass inside the tank The cover of the reactor is constructed of polyester or ebonite-coated panels. The phosphate rock is fed by a special duct within a cylindrical shroud at one or two points, according to the size of the tank, and into the turbulence zone of the central agitator on the opposite side to the gas extraction hood. The sulfuric acid is introduced into one, or several, independent discs fixed to the drive shafts of some of the surface coolers. The proprietary equipment distributes the acid so evenly over the entire surface of the tank that 98% acid can be introduced directly without prior dilution. There is no risk of local sulfuric acid concentration excess or temperature peaks, which can adversely affect the crystallization. 

The sensation of balance, and thus the ability to maintain equilibrium, is regulated by a complex interaction of bodily systems that includes the inner ears, the eyes, skin pressure receptors, muscle and joint sensory receptors, and the CNS (brain and spinal cord). The cause of motion sickness is generally considered to be a mismatch of visual and inner ear sensations. The eyes observe where the body is in space (e.g., upside down, right side up, etc.) and also directions of motion. Within the inner ear, these sensations pertain specifically to the vestibular complex, including the vestibule (which includes a pair of membranous sacs containing receptors for the sensation of gravity and linear acceleration) and the semicircular canals (which contain ducts with receptors that are stimulated by rotation of the head and detect angular acceleration). The CNS receives visual and vestibular sensory information and compares the... 

Here, we have denoted the bodily rotation of the entire molecule as Qs in order to indicate that its action also involves the nuclei, as opposed to C3, which is reserved for electrons. In the expression of Eq. (4.1), Ra is replaced by Rb, or... 

In this case, the only contribution to the trace comes from the distortion of A, which is mapped onto minus itself hence, x(ai) = -1. The resulting character string also has norm 12, but in this case it decomposes into A2 + E. As shown in Fig. 4.2, the A2 component is the sum of the three distortions, which corresponds to a bodily rotation of the molecule around its vertical axis. The E components are given by... 

Table 5.1 Embedding of the Csu point group in the Longuet-Higgins group. The symmetry elements of the point group act on the electrons. They are identified as the product of nuclear permutations, inversion of all particles (star operation), and bodily rotations of aU particles (Q operators) along particular directions...

Chemists are more used to the operational definition of symmetry, which crystaUo-graphers have been using long before the advent of quantum chemistry. Their ball-and-stick models of molecules naturally exhibit the symmetry properties of macroscopic objects they pass into congruent forms upon application of bodily rotations about proper and improper axes of symmetry. Needless to say, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles, nuclei, and electrons. It is hard to see how bodily rotations, which leave all interparticle distances unaltered, could affect in any way the study of molecular phenomena that only depend on these internal distances. Hence, the purpose of the book will be to come to terms with the subtle metaphors that relate our macroscopic intuitive ideas about symmetry to the molecular world. In the end the reader should have acquired the skills to make use of the mathematical tools of group theory for whatever chemical problems he/she will be confronted with in the course of his or her own research. 

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