Two-scale system

The fuel cell is basically a two-scale system. The small and large scales are determined, respectively, by membrane-electrode assembly (MEA) thickness and by the length of the feed channel. The Q3D model is designed to investigate the interplay of small- and large-scale processes in PEFC/DMFC, so that the fully 3D model of the cell is split into a model of a cell cross section (internal model) and a model of the flow in the channel (channel model). The two models are coupled via the local current density along the channel and the overall Q3D solution is obtained by iterations. 

A fuel cell is a two-scale system the characteristic in-plane size of a typical cell is about 10 cm, while the thickness of the membrane-electrode assembly... 

For the purpose of physical modeling of CL operation, it is expedient to treat the layer as a two-scale system as illustrated in Figure 4.1. Referring to the hierarchical scheme in Figure 1.16, the emphasis will be on the two rightmost scales. At the mesoscopic scale, operation is determined by the properties of agglomerates composed... 

It follows that there are two kinds of processes required for an arbitrary initial state to relax to an equilibrium state the diagonal elements must redistribute to a Boltzmaim distribution and the off-diagonal elements must decay to zero. The first of these processes is called population decay in two-level systems this time scale is called Ty The second of these processes is called dephasmg, or coherence decay in two-level systems there is a single time scale for this process called T. There is a well-known relationship in two level systems, valid for weak system-bath coupling, that... 

These processes are very rapid and allow the preparation of inorganic supports in one step. This technique allows large-scale manufacturing of supports such as titania, fumed silica, and aluminas. Sometimes the properties of the material differ from the conventional preparation routes and make this approach unique. Multicomponent systems can be also prepared, either by multimetallic solutions or by using a two-nozzle system fed with monometallic solutions [22]. The as-prepared powder can be directly deposited onto substrates, and the process is termed combustion chemical vapor deposition [23]. 

To complete the discussion of the second-order interaction between tunneling centers, we note that the corresponding contribution to the heat capacity in the leading low T term comes from the ripplon-TLS term and scales as 7 +2 where a is the anomalous exponent of the specific law. Within the approximation adopted in this section, a = 0. However, it is easily seen that the magnitude of the interaction-induced specific heat is down from the two-level system value by a factor of 10(a/ ) ([Pg.188]

The two-component lipid models were also characterized in the absence of sink conditions (Table 7.8). Comparisons between models 7.0 (Table 7.7) and 1.0 (Table 7.5) suggest that negative charge in the absence of sink causes the permeabilities of many of the bases to decrease. Exceptions are quinine, prazosin, primaquine, ranitidine, and especially metoprolol. The inclusion of 0.6% PA causes Pe of metoprolol to increase nearly 10-fold, to a value twice that of propranolol, a more lipophilic molecule than metoprolol (based on the octanol-water scale). Naproxen and ketoprofen become notably more permeable in the two-component system. Surprisingly, the neutral progesterone becomes significantly less permeable in this system. 

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