Irreducible nets

From a computational viewpoint, the presence of recycle streams is one of the impediments in the sequential solution of a flowsheeting problem. Without recycle streams, the flow of information would proceed in a forward direction, and the cal-culational sequence for the modules could easily be determined from the precedence order analysis outlined earlier. With recycle streams present, large groups of modules have to be solved simultaneously, defeating the concept of a sequential solution module by module. For example, in Figure 15.8, you cannot make a material balance on the reactor without knowing the information in stream S6, but you have to carry out the computations for the cooler module first to evaluate S6, which in turn depends on the separator module, which in turn depends on the reactor module. Partitioning identifies those collections of modules that have to be solved simultaneously (termed maximal cyclical subsystems, loops, or irreducible nets). 

For unambiguous preparations, the theory reveals limitations on the amount of work that can be done by a system adiabati-cally and without net changes in parameters. These limitations are due to irreducible dispersions inherent in the state of the system. They are maximal when the dispersions correspond to a stable equilibrium state. 

These functions assume that net latency is derived from diffusion time to receptors plus irreducible reaction time. The small number of data points hardly provides a rigorous test of this recently elaborated model (9). The model has, however, already proved quite useful in descriptions of latency from single olfactory units, and merits thorough psychophysical testing. 

Permeability, md Net Thickness, ft Gross Thickness, ft Irreducible Water Sat., % Residual Oil Sat., % Reservoir Temperature, T... 

As remarked above, Mulliken populations ( gross or net ) commonly fail to satisfy the physical constraints (4a, b). The natural orbitals (NOs) 0 of equation (I) are intrinsically best possible for condensing maximum occupancy in the smallest possible number of orbitals. However, they are rather unsuitable for chemical analysis, since they transform as irreducible representations of the full symmetry group of F (the symmetry of the Hamiltonian) and thus appear delocalized over all nuclear centers and highly non-transferable. In this respect, NOs are similar to canonical molecular orbitals (to which they reduce in the uncorrelated Hartree-Fock limit). In contrast, the NBOs retain the high occupancy of NOs, but have local one-and two-center character that takes advantage of the high transferability of localized electron pairs of the molecular Lewis structure. 

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