Steady-state phenomenon

Sample-standard comparison is more applicable in MC-ICP-MS, in which instrument mass fractionation is fundamentally a steady state phenomenon (Marechal et al. 1999). This method has been used successfully for some non-traditional stable isotopes, particularly involving Fe, in which analyses of samples are bracketed by standards to cope with systematic instrumental drift (e.g., Zhu et al. 2002 Beard et al. 2003). However, other methods have been used for Mo stable isotope work published to date because of concerns about non-systematic changes in instrument mass fractionation, particularly arising from differences in matrices, between samples and standards. Such concerns are more acute for Mo than for Fe and many other elements because Mo is a trace constituent of most samples, increasing the challenge of rigorous, high-yield sample purification. 

Once the hydrocarbons have been solubilized in the formation water, they move with the water under the influence of elevation and pressure (fluid), thermal, electroosmotic and chemicoosmotic potentials. Of these, the fluid potential is the most important and the best known. The fluid potential is defined as the amount of work required to transport a unit mass of fluid from an arbitrary chosen datum (usually sea level) and state to the position and state of the point considered. The classic work of Hubbert (192) on the theory of groundwater motion was the first published account of the basinwide flow of fluids that considered the problem in exact mathematical terms as a steady-state phenomenon. His concept of formation fluid flow is shown in Figure 3A. However, incongruities in the relation between total hydraulic head and depth below surface in topographic low areas suggested that Hubbert s model was incomplete (193). Expanding on the work of Hubbert, Toth (194, 195) introduced a mathematical mfcdel in which exact flow patterns are... 

Early diagenesis is typically described as a steady-state phenomenon however, unless very long-term geological timescales are considered, steady-state conditions are generally not common in shallow turbid environments such as estuaries. There are many factors that contribute to these non-steady-state conditions, such as variations in sedimentation rate, inputs of organic matter, chemistry of bottom waters and sediments, bioturbation rates, and resuspension (Lasagna and Holland, 1976). Consequently, numerous attempts... 

We call this high sensitivity of the recycle flowrates to small disturbances the snowball effect. We illustrate its occurrence in the simple example below, It is important to note that this is not a dynamic effect it is a steady-state phenomenon. But it does have dynamic implications for disturbance propagation and for inventory control. It has nothing to do with closed-loop stability. However, this does not imply that it is independent of the plant s control structure. On the contrary, the extent of the snowball effect is very strongly dependent upon the control structure used. 

Lastly it should be emphasized that the primary photoproducts formed directly from the excited states might themselves be very reactive species. These may react subsequently to give stable products by unimolecular or more complex mechanisms. Continuous photolysis experiments which use low intensity excitation generate only small steady state concentrations of excited states and reactive intermediates, so only stable products or a steady state phenomenon such as Iruninescence are generally observed. Flash photolysis techniques, which prepare transient species in non-steady state concentrations, often allow direct observation of such species. 

The two frequency functions shown In the bottom two frames of Figure 7 correspond to different steady-state populations growing at approximately the same overall population growth rates as those shown In the two middle frames. These different steady states were achieved by different start-up procedures of the reactor and seem to be connected with some unusual cell clumping phenomenon when reactor start-up Initiates with a significant glucose limitation of growth. Additional Information on this multiple steady-state phenomenon and on Its manifestation In other types of measurements Is available elsewhere (9). 

In the lipid bilayer systems, since the membrane molecules are arranged in such a way that the charged groups face a water phase and the interior of the membrane is a hydrocarbon phase, the contribution of surface potential to the membrane potential is important. It should be mentioned that the contribution of surface potential to the membrane potential, as discussed above, is generally a transient one in these systems. However, since the electrical conductance due to ion permeation across the lipid bilayer membrane is very low, we can observe the transient potential difference as a quasi-steady state phenomenon. However, if a constant ion distribution is restored by a transport process with a nonelectrical current (active transport) and maintained continuously, the above membrane potential process could become a steady state process. 

Now if the reflux is increased back to 0.09 kmol/s, the column does not converge to the same steady state that it had previously at this flow rate. The flow rate must be increased to about 0.11 kmol/s to reestablish the desired low water content in the bottoms. This multiple steady-state phenomenon is one of the severe complexities that simulations of distillation columns experience when highly nonideal VLLE relationships are involved. 

The diffusion coefficient and the diffusion length are fundamental macroscopic properties of a material which are useful in the one-velocity formulation. Both quantities can be measured directly in the laboratory by suitable experiments. The direct measurement of the diffusion coefficient, however, entails the use of a pulsed beam of neutrons. Inasmuch as this experiment involves a time-dependent phenomenon, a discussion of the experiment will be deferred until after a suitable model has been developed for the analysis of nonstationary problems in neutron diffusion. An experiment for the direct determination of the diffusion length, however, is based on a steady-state phenomenon, and the important features of this experiment can be displayed by means of the models and concepts already developed. Because of the close relationship between the parameters L and D, it would be desirable to examine the techniques for their measurement simultaneously. This is not possible because of the complications mentioned above thus for the present we confine our attention to the study of the diffusion length and an experiment for its measurement. 

The flat film process, in which an extruded sheet is drawn up on a roll, is a two-dimensional analog of melt spinning, and the dynamical equations and instabilities are essentially the same. The finite aspect ratio of the film die and the presence of an edge on the extruded sheet introduce stresses that cause necking in of the sheet. This is a steady-state phenomenon that does not seem to have major dynamical implications. 

Because the snowball effect is a steady-state phenomenon, it can be analyzed by considering a steady-state model. We first consider two alternatives for controlling reactor level Hr (Luyben, 1994). For Alternative 1 in Fig. G.la, Hr is controlled by manipulating the column feed rate F (i.e., the reactor effluent rate). For Alternative 2 in Fig. GJb, Hr is allowed to float while F is held constant. This strategy is possible because, in theory, the reactor level in this structure is self-regulating (Larsson et al., 2003). For the moment, we assume that the plant production rate is established either upstream or downstream of the plant and analyze these two simple cases to see what insight can be obtained. Later, we consider the implications of setting production rate within the plant. 

An important point should be emphasized here— namely, that the snowball effect in D and F, while resulting from a particular control structure, is a steady-state phenomenon. In that sense, it is similar to the RGA, which is also a measure of steady-state sensitivities. Luyben (1994) suggested an alternative control method that was intended to reduce the snowball effect in D and F. We investigate a variation of his proposed method next. 

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