Hierarchical reference theory

A more fundamental but much more complex numerical approach is provided by the hierarchical reference theory (HRT). °° In the HRT the numeral implication of the renormalization transformation is applied on a microscopic model of the fluid. One starts from a reference system with short-range repulsive interactions and then formulates a hierarchy of integral equations accounting for successively longer-range fluctuations. The theory has also been extended to fluid mixtures. " The HRT provides estimates for both... 

FIGURE 75.1 The Elemental Resource Model contains multiple hierarchical levels. Performance resources (i.e., the basic elements) at the basic element level are finite in number, as dictated by the finite set of human subsystems and the finite set of their respective dimensions of performance. At higher levels, new systems can be readily created by configuration of systems at the basic element level. Consequently, there are in infinite number of performance resources (i.e., higher-level elements) at these levels. However, rules of General Systems Performance Theory (refer to text) are applied at any level in the same way resulting in the identification of the system, its function, dimensions of performance, performance resource availabilities (system attributes), and performance resource demands (task attributes). 

The examples to be presented illustrate the diversity of fields of applications, but they are mentioned in outline form only. Many biological phenomena used to be modelled by real or formal kinetic models. A biochemical control theory that is partially based on non-mass-action-type enzyme kinetics seems to be under elaboration, and certain aspects will be illustrated. A few specific models of fluctuation and oscillation phenomena in neurochemical systems will be presented. The formal structure of population dynamics is quite similar to that of chemical kinetics, and models referring to different hierarchical levels from elementary genetics to ecology are well-known examples. Polymerisation, cluster formation and recombination kinetics from the physical literature will be mentioned briefly. Another question to be discussed is how electric-circuit-like elements can be constructed in terms of chemical kinetics. Finally, kinetic theories of selection will be mentioned. 

In coupled-cluster theory, the wave function is written as an exponential of a cluster operator (13.2.4) acting on a single-determinant reference state (13.2.3). In constructing the wave function, the excitations included in the cluster operator are not selected individually. Rather, a hierarch -of approximations is established by partitioning the cluster operator into classes comprising all single (one-electron) excitations, all double (two-electron) excitations, all triple (three-electron) excitations, and so on. We may then write the cluster operator in the form... 

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