Steady states reconstruction

Let us take a weakly ergodic network iV and apply the algorithms of auxiliary systems construction and cycles gluing. As a result we obtain an auxiliary dynamic system with one fixed point (there may be only one minimal sink). In the algorithm of steady-state reconstruction (Section 4.3) we always operate with one cycle (and with small auxiliary cycles inside that one, as in a simple example in Section 2.9). In a cycle with limitation almost all concentration is accumulated at the start of the limiting step (13), (14). Hence, in the whole network almost all concentration will be accumulated in one component. The dominant system for a weekly ergodic network is an acyclic network with minimal element. The minimal element is such a component Amin that there exists an oriented path in the dominant system from any element to Amin- Almost all concentration in the steady state of the network iV will be concentrated in the component Amin-... 

In contrast, at room temperature, the reconstructed fluorescence spectra were found to be identical to the steady-state spectrum, which means that solvent relaxation occurs at times much shorter than 1 ns in fluid solution. 

Fig. 3. Reconstruction of the transient absorption spectra of HPTA in DCM in the presence of 9xlO 3 M DMSO at different pump-probe delays. The time-zero absorption and gain bands of the photoacids are moving toward each other following the relaxation of the solute-solvent interactions to their steady-state values. Full lines are the superposition of the individual absorption and gain bands of HPTA.

The time-resolved emission spectra were reconstructed from the fluorescence decay kinetics at a series of emission wavelengths, and the steady-state emission spectrum as described in the Theory section (37). Figure 4 shows a typical set of time-resolved emission spectra for PRODAN in a binary supercritical fluid composed of CO2 and 1.57 mol% CH3OH (T = 45 °C P = 81.4 bar). Clearly, the emission spectrum red shifts following excitation indicating that the local solvent environment is becoming more polar during the excited-state lifetime. We attribute this red shift to the reorientation of cosolvent molecules about excited-state PRODAN. 

Figure 10 displays the steady state invading liquid water fronts corresponding to increasing capillary pressures from the primary drainage simulation in the reconstructed CL microstructure... 

Figure 13. 3-D liquid water distributions in the reconstructed CL microstructure from the steady state flow simulation at equilibrium.

The steady-state flow numerical experiment was primarily designed to evaluate the phasic relative permeability relations. The numerical experiment is devised within the two-phase lattice Boltzmann modeling framework for the reconstructed CL microstructure, generated using the stochastic reconstruction technique described earlier. Briefly, in the steady-state flow experiment two immiscible fluids are allowed to flow simultaneously until equilibrium is attained and the corresponding saturations, fluid flow rates and pressure gradients can be directly measured and correlated using Darcy s law, defined below. 

Thermal stress calculations in the five cell stack for the temperature distribution presented above were performed by Vallum (2005) using the solid modeling software ANSYS . The stack is modeled to be consisting of five cells with one air channel and gas channel in each cell. Two dimensional stress modeling was performed at six different cross-sections of the cell. The temperature in each layer obtained from the above model of Burt et al. (2005) is used as the nodal value at a single point in the corresponding layer of the model developed in ANSYS and steady state thermal analysis is done in ANSYS to re-construct a two-dimensional temperature distribution in each of the cross-sections. The reconstructed two dimensional temperature is then used for thermal stress analysis. The boundary conditions applied for calculations presented here are the bottom of the cell is fixed in v-dircction (stack direction), the node on the bottom left is fixed in x-direction (cross flow direction) and y-direction and the top part is left free to... 

The steady state reaction of NO with H2 and NH3 on Pt(l 0 0) has been studied using REMPI detection of the N2 product state distributions [134]. These reactions show very complex kinetics, with strongly coverage dependent reaction rates which lead to kinetic oscillations [135] and explosive desorption [136]. This surface also shows a phase transition between the clean surface hex reconstructed phase and... 

Fio. 9. Streamlines showing steady-state velocity profile during single-phase flow in a reconstructed porous medium. 

We have used the spectral reconstruction method to obtain a time-resolved fluorescence spectrum [13] When the fluorescence up-conversion method is used, the relative intensity between each wavelength becomes uncertain because the angle of the nonlinear crystal has to be tuned at each wavelength of observation. However, the intensity of the fluorescence /(A, (), at a given time t and wavelength A, can be obtained from the normalized fitted decay series D(t, A) and intensity of the steady-state fluorescence /0(A) ... 

The method used to reconstruct nerve behaviour derives directly from that originally proposed by Hodgkin and Huxley (18) for squid axons. The parameters used in these equations have been taken from earlier experiments on isolated cockroach axons (19-20). To reproduce the effects of the insecticide, a set of new equations, the "p" equations, have been derived from the above voltage-clamp experiments. The steady-state values of p as well as the values of the time constants used in the reconstructions are illustrated in Fig.5. It is assumed that activation of the slow channels is a first order process and that these channels do not inactivate. 

Equation 6.14 provides a formal connection between creep crack growth and the kinetics of creep deformation in that the steady-state crack growth rates can be predicted from the data on uniaxial creep deformation. Such a comparison was made by Yin et al. [3] and is reconstructed here to correct for the previously described discrepancies in the location of the crack-tip coordinates (from dr/2 to dr) with respect to the microstructural features, and in the fracture and crack growth models. Steady-state creep deformation and crack growth rate data on an AlSl 4340 steel (tempered at 477 K), obtained by Landes and Wei [2] at 297, 353, and 413 K, were used. (AU of these temperatures were below the homologous temperature of about 450 K.) The sensitivity of the model to ys, N, and cr is assessed. 

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