Imposed flux

Comparison of the integration of this last conservation equation with the direct simulation of an uncoupled neural population with a given distribution of states (v, u) at the initial time provides a validation for the simplified version of the model. Then adding the imposed flux accounting for connectivity allows us to simulate a large population of Izhikevich neurons with a given pattern of connectivity (number of afferents per neuron and delays kernel). 

Finally we can write the expression of the interaction flux using a mean-field approximation for the conductance and using the value of the average individual spike reception rate o(t ) previously given, the complete expression of the imposed flux is ... 

Consider now a more interesting type of stimulus involving a periodically varying flux (Fig. 4.26). After representing the imposed flux by a cosine function... 

If the cell is connected to an external power source, electrolysis takes place. The system, called an electrochemical cell, is now driven away from the thermodynamical equilibrium by an imposed flux, the electrical current. Internal entropy is produced. With increasing current, the terminal voltage will increase (Fig. 3.2(b)). 

A snapshot of a typical result is reported in Figure 10.14. By ehanging the imposed flux through the membrane, the effect of gas extraction on the bubble diameter and bubble size distribution can be investigated. 

Determination of the Stochastic Potential in Chemical Systems with Imposed Fluxes... 

Consider the chemical system in (11.1) with the species being either ions or neutrals the system is in a reaction chamber in a non-equilibrium stationary state. We impose a flux of species Ai, J = k A[, into the reaction chamber with <5+ and Q- held constant and thereby move the chemical system to a different non-equilibrium stationary state with different concentrations of the reacting species Ai, Bi, A, B2- This procedure allows the sampling of different combinations of the reacting species by means of the imposition of different fluxes of these reactants. These combinations represent different non-stationary states in the absence of imposed fluxes, but with the imposed fluxes they are stationary states and hence measurements may be made without constraints of time. If we would attempt to measure concentrations in non-stationary states then the measurement technique would have to be fast compared to the time scale of change of the concentrations due to chemical reactions. 

Let the imposed flux be J = k X. The stationary solution of the lowest order eikonal approximation of the master equation for the system (11.15) with the imposed flux is... 

At a stationary state of the system with imposed flux we have d

[Pg.106]

Thus from measurements with imposed flux we obtain the derivative of the stochastic potential for the system without imposed flux, but we need kinetic information, the rate coefficients in as well. 

However, the use of different Lj[j values at successive boundaries will impose flux differences across each zone, which must be balanced by internal precipitation. The net amount of this internal precipitation is easily found by a simple modification of the procedure outlined above simply solve eq. (1.4) for the total flux difference across the mantle, in effect integrating the internal precipitation throughout the mantle, using the restrictions imposed on the VTij[ by equilibrium with B, and remembering that any reaction within the mantle must involve mineral B only. This procedure will also give a local value for the fluxes at the AB/B boundary/ which may be used in eq. (1.4) to obtain the reaction at the AB/B boundary as before. 

The time of the depletion event is given by the ability of the solution to maintain an imposed flux, which bears some analogy to the mechanisms of bio-uptake and ecotoxicology in environmental systems. This class of sensors therefore gives information on the concentration of kinetically available species in solution. The technique is also promising for effecting localized titrations to assess information on total acidity or alkalinity (the latter is detectable by a controlled current release of hydrogen ions from a pH sensitive membrane electrode). 

Submerged membranes are typically operated at fixed (imposed) flux (/, ) This means that changes due to deposition/fouling are reflected in changes to TMP. So we can write... 

Equation (10.10) shows that tc is very sensitive to the imposed flux and inversely proportional to the feed concentration Ch- Thus, a 40% increase in flux could almost halve the cycle time. 

Figure 10.17 Effect of imposed flux on TMP profiles for submerged hollow fibers. Yeast 5 g/L with bubbling (Chang and Fane, 2002).

Figure 10.18 Flux distribution at steady state for different imposed flux conditions (a) /i niax < Ami and (b) J u < Jcm, Amax > Jca (Chang and Fane, 2002).

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