Global domain

As already discussed, variations of a field unknown within a finite element is approximated by the shape functions. Therefore finite element discretization provides a nat ural method for the construction of piecewise approximations for the unknown functions in problems formulated in a global domain. This is readily ascertained considering the mathematical model represented by Equation (2.40). After the discretization of Q into a mesh of finite elements weighted residual statement of Equ tion (2.40), within the space of a finite element T3<, is written as... 

In order to establish an isoparametric mapping between the master element shown in Figure 2.23 and the elements in the global domain (Figure 2.20) we use the elemental shape funetions to formulate a transformation function as... 

Moore, J., Doney, S., Kleypas, J., Glover, D., and Fung, I. (2002). An intermediate complexity marine ecosystem model for the global domain. Deep Sea Res. II49, 403—462. 

Archer D. E., Morford J. L., and Emerson S. (2001) A model of suboxic sedimentary diagenesis suitable for automatic tuning and gridded global domains. Global Biogeochem. Cycles (in press). 

Figure 4.12. (Top ) The binary phase diagram of didodecyl phosphatidylethanolamine -water mixtures. (Adapted from [15].) Single-phase regions are white, two-pha% regions shaded. The thermotropic behaviour at about 20% w/w water is illustrated by die line ABC. (Bottom ) The trajectory of the line ABC in the local/global domain (see previous figure), showing the variation of molecular shape as a function of temperature for this l d. The phase diagram can be reconciled with the local/global behaviour if the "lamellar" (L) phase is in fact a mesh structure, i.e. porous lamellae.

In most cases, the complex array of interactions at work within an actual surfactant-water mixture leads to variations of the surfactant parameter with surfactant dilution and temperature. In general then, the phase behaviour of a binary surfactant-water mixture follows a curved trajectory through the local/global domain plotted in Fig. 4.11. If these variations in molecular conformation are small, the phase progression with water dilution is expected to follow a nearly-vertical line in the plot if the molecular architecture is sensitive to these external parameters, die succession of phases with water dilution is more nearly horizontal. 

Figure 4.13. (Left ) The binary phase diagram of AOT-water mixtures (after (17,18]). The lyotropic behaviour at room temperature is illustrated by the line ABC. (Right) The trajectory of die line ABC in the local/global domain.

While cyberspace generally refers to the global domain of interconnected computing systems, in this work we focus on the specific cyber domain that supports ballistic missile defense in the United States. Thus when we refer to the Cyber OODA loop we are referring to the specific decision-making process used to defend the BMD mission from cyber attack. 

By substituting Equation (2.29) in Equation (2.30), we can obtain a relation that provides the conduction efficiency of the global domain s j) which is formed by several subdomains of smaller scale (Equation (2.31)) ... 

To normalize and generalize the results in this section, calculated resistivities are used to estimate a conduction efficiency r f). As conductivity is the inverse of resistivity, the CL s effective conductivity is the inverse of the effective resistivity value kgu = p fl. Then the conduction efficiency pk is calculated by comparing the effective conductivity with a reference or nominal conductivity, as described by Equation (2.37). By substituting Equation (2.36) in Equation (2.37), one can obtain a relation that provides the conduction efficiency of the global domain which is formed by several subdomains (Equation (2.38)) ... 

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