Diffusion network

In addition, the brainstem contains a diffuse network of neurons known as the reticular formation. This network is best known for its role in cortical alertness, ability to direct attention, and sleep. It is also involved with coordination of orofacial motor activities, in particular those involved with eating and the generation of emotional facial expressions. Other functions include coordination of eating and breathing, blood pressure regulation, and response to pain. 

Figure 3. Form factor for a) star graphs numerics (red) versus the power series expansion (15) (green) b) diffusive network (in 2 d) deviations occur for small r, see inset. 

K. G. Kirby and M. Conrad, The enzymatic neuron as a reaction-diffusion network of cyclic nucleotides, Bull Math. Biol, 46, 765-783 (1984). 

To construct the pertraction network, the particular reaction networks should be added via 0 junctions to three linear networks corresponding with the processes of diffusion of C2A, C2B, and CH carrier species. The resulting reaction-diffusion network, as presented in Figure 13.6, consists of four coupled loops representing the pertraction of A " ", and H" " cations. The loops are coupled by common capacitances Aj, Bj, and Hj (i = f, s) and by the capacitances CHj and CH for a reacting or diffusing acidic form of the carrier. From the network in Figure 13.6, all the model equations used further in numerical calculations can be deduced with the help of Kirchhoff s law for a 0 junction (KCL) ... 

The mechanism of the competitive pertraction system (CPS) is presented schematically in Fig. 5.4 together with the compartmental model necessary for constructing the reaction-diffusion network. The simple flat-layered bulk liquid membrane of the thickness En and interface area S separates the two reservoirs (f, feed and s, stripping) containing transported divalent cations A2+ and B2+ (most frequently Zn2+ and Cu2+ or Ca2+ and Mg2+) and/or antiported univalent cations H+. At any time of pertraction t, their concentrations are [A]f, [B]f, and [H]f and [A]s, [Bj, and [H]s, for the feed and stripping solution, respectively. The hydrophobic liquid membrane contains a carrier of total concentration [C]. Its main property is the ability to react reversibly with cations at respective reaction zone and to diffuse throughout the liquid membrane phase. 

The reaction-diffusion network, as presented in Fig. 5.5, consists of four coupled loops representing the pertraction of A-+, B2+, and H+ cations. All model equations used further in numerical calculations can be deduced with the help ofKirchhotTs law for a 0 junction (KCL) ... 

The measurement of diffusion rates as functions of various activities, in particular oxygen fugacity, is extremely important to clarifying the diffusion mechanisms and aid in extrapolation. The work of Ryerson et al. (1989) is the only geochemical example of such type of work. Questions of concern include under what conditions does the /02-dependence occur, and what does it tell us about the main mechanism of O2 transport (e.g. permeation versus diffusion, network versus molecular oxygen diffusion etc.). 

Fu AI, Mauro JC. Mutual diffusivity, network dilation, and salt bath poisoning effects in ion-exchanged glass. Journal of Non-Crystalline Solids, 2013 363 199-204. 

Rubberlike elasticity, where the local freedom of motion associated with small-scale movement of chain segments is retained but large-scale movement (flow) is prevented by the restraint of a diffuse network structure. 

In (5.74), the box D represents the combination of the partial diffusion networks (5.73) and its Na -counterpart whereas Cg/F is an electric capacity per area with a constitutive relation... 

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