Bubble diagrams

Figure 8. Bubble diagram of concentrations (milligrams per liter) of chemical components in well 138 (Figure 3) showing changes with time in wells of different depths the upper scale bar (bubble diameter) is the concentration of the species as depicted by bubble, the vertical axis is the elevation of the screened interval of the well, and the horizontal axis is the days since drawdown A, sulfate and B, arsenic.

The standard RPA bubble diagram summation prevails for static processes. The result is... 

Third-order calculations are considered in the next section. This is followed by a brief discussion of the computation of higher-order terms and of the evaluation of bubble diagrams which are required when molecular properties are calculated or when a reference function other than the closed-shell Hartree-Fock function is employed. The impact of the new generation of computers, which have vector processing capabilities, on many-body perturbative calculations is discussed very briefly in the final section. 

Bubble Diagrams.—The bubble diagrams which are shown in Figures 13 and 14 are required when the reference function for a closed-shell system is not defined by the matrix Hartree-Fock model, when a restricted Hartree-Fock reference... 

Figure 23 Bubble diagrams which arise when the Breit interaction is treatedperturbatively...

Fig. 33. (a) Dyson equation for the pseudofermion propagators of CEF states n, m (broken lines). Phonons are indicated by wavy lines. Open circles represent the magnetoelastic interaction vertex, (b) Bubble diagram for the dynamical magnetic susceptibility using renormalized propagators. Open squares represent the dipolar operator J. 

Once all alternative block diagrams have been thoroughly considered and reviewed with hospital personnel, a single direction can be established for more detailed schematic design. Alternative layouts for each department are studied using drawings called bubble diagrams. 

Figure 38.14 shows a typical bubble diagram. Normally, several alternative arrangements are studied using diagrams such as these. Bubble diagrams can help the team study by showing... 

Fig. 6. RPA diagrams for the effective interaction J k — k ) between quasiparticles with opposite spins. The bare instantaneous interaction is denoted by I (dashed line) as in eq. (11). Contribution from polarisation (bubble) diagrams contains odd number and from (maximally crossed) exchange diagrams contain any number of interaction lines (/). For equal quasiparticle spins the RPA yields only a sum of bubble diagrams with an even number of interaction lines.

In Table 6.1 we have evaluated all second-, third-, and fourth-order diagrams using our rules. By convention, the first-order bubble diagram is... 

Proteome maps (or proteomics maps) are arrived at by an experimental approach, which simultaneously combines electrophoresis and chromatography, and separates thousands of different proteins from cellular material by charge and by mass. The results are obtained as collection of spots on 2-D films, from which one can extract the (x, y) coordinates of the protein spots and, by measuring the density of the spot, their abundance. Snch results one can use to construct a bubble diagram, 2-D map in which the size of the bubbles represents the abundance of proteins, and... 

Fig. 6 Bubble diagram depicting maximum measured surface tension depression for organic surfactant species in aqueous solution (from Tables 2, 3, 4 and 7) as a function of average carbon oxidation state (OSc) in the molecule and number of carbon atoms (iic) [296]. The size of the bubble is proportional to the maximum measured departure from the surface tension of water (72 mN m ) for each species. Also shown are typical values of (OSc) and c for atmospheric organic aerosol material as classified from Aerodyne Aerosol Mass Spectrometer measurements. HOA indicates hydrocarbon-like organic aerosol, BBOA is biomass buming aerosol, SV-OOA is semivolatile oxidized organic aerosol, and LV-OOA is low-volatility oxidized organic aerosol...

This type of the system decomposition models is often referred to as the Bubble Diagram , bubbles represent the subsystems and rectangles represent the constituents at lower level of decompositiom Directed lines are interfaces that link up subsystems and constituents into a system. 

Fig. 3.4. Lowest-order diagrams associated with cation-anion orbital hybridization. Unlike the representations used in the many-body problem, the diagram vertices - a dot for an anion and a rectangle for a cation - here symbolize the matrix elements of Gj, while the arrowed lines indicate hopping processes associated with Hnd- Only bubble diagrams of the cl - and c3-types are kept to derive the local charge transfer.

Given the above functional and integrity requirements, a sketch (i.e., a bubble diagram as shown in Figures 4, 6 and 8) was developed for each SIF to ... 

The bubble diagrams were then utilized to develop a fault tree for each SIF using commercially available software. The output of the fault tree analysis software documents the SIF PFD (see Figures 5, 7, and 9). At this point, the calculated PFD was compared to the required PFD (see Table 7, column 10) where the calculated PFD failed to meet Table 7 requirements, the conceptual design was altered accordingly. 

The SIS logic solver has a claim limit of SIL 3, which addresses failures of hardware, architectural requirements (fault tolerance) and the embedded software. Note that systematic failures of application software were not addressed in the certification of the logic solver. Systematic logic solver application software failure issues were addressed by shadowing the logic in the BPCS (see bubble diagrams Figures 4, 6, and 8). The BPCS was used to reduce the systematic failures of SIS application software however, the contribution of the BPCS hardware to the PFD has not been included in the fault tree analysis for each SIF. 

Figure 4 - SIF S-1 Bubble Diagram showing the PFD of each SIS device...

SIL verification calculations (i.e., PFD) forSIFs including bubble diagrams... 

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