Terms that begin with numbers

We need to begin with a brief review of atomic structure. Atoms consist of relatively compact nuclei containing protons and neutrons. At some distance from these dense nuclei each atom has electrons moving in a cloud around the central nucleus. The electrons move in shells or orbitals or probability waves (different words derived from more or less classic or quantum mechanical terms of reference) around the nucleus, and the number of electrons circulating in these orbitals depends on the element in question. Four things are particularly important for flow cytometrists to understand about these electrons First, atoms have precisely defined orbitals in which electrons may reside. Second, an electron can reside in any one of the defined orbitals but cannot reside in a region that falls between defined orbitals. Third, the energy of an electron is related to the orbital in... 

The breakup or bursting of liquid droplets suspended in liquids undergoing shear flow has been studied and observed by many researchers beginning with the classic work of G. I. Taylor in the 1930s. For low viscosity drops, two mechanisms of breakup were identified at critical capillary number values. In the first one, the pointed droplet ends release a stream of smaller droplets termed tip streaming whereas, in the second mechanism the drop breaks into two main fragments and one or more satellite droplets. Strictly inviscid droplets such as gas bubbles were found to be stable at all conditions. It must be recalled, however, that gas bubbles are compressible and soluble, and this may play a role in the relief of hydrodynamic instabilities. The relative stability of gas bubbles in shear flow was confirmed experimentally by Canedo et al. (36). They could stretch a bubble all around the cylinder in a Couette flow apparatus without any signs of breakup. Of course, in a real devolatilizer, the flow is not a steady simple shear flow and bubble breakup is more likely to take place. 

For the mathematics of this, consider the discrete equation resulting from the Euler method, as in (4.8). Note that the new point, yn+i is formed from the old point yn by the addition of a term, here St f(yn). With RK, these terms are given the symbols fcj, there are from one to several of them, and they are added in a weighted manner. The procedure is to generate a number of these k s. One begins with an Euler step,... 

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