Marginal regime

Fig.22. Evolution of the critical shear rate y at the onset of the marginal regime as a function of the surface density in the grafted surface layer, o, for mP=970 kg mol-1, and mN= 96 kg mol-1. For 0.003

In terms of shear stresses, the onset of the marginal regime corresponds to the stress... 

In the concentrated and marginal regimes of fig 5,3 a mean-field description, which neglects any spatial fluctuations, is appropriate. In these regimes, the solution is homogeneous and there is no chain-length dependence. Neither does the persistence p of the chains play a role since the Floiy-Huggins expressions do not contain the chain flexibility. This is so because the flexibility is assumed to be the same in the solution and in the reference state, so that p cancels in the entropy difference between the two states. 

For tp > 5 " the strong density fluctuations in the semidilute regime disappear, and in the marginal regime the solution may again be described by a mean-fleld theory, as discussed in 5.2c. 

Actually, we have used the term semidilute in a loose sense here (hence the quotation marks) it denotes neither dilute, nor concentrated. Polymer scientists distinguish a semidilute and a marginal regime. Scaling... 

It should be noted carefully that Pearson s analysis still contains the assumption that instability sets in only by a stationary marginal state, which of course excludes the actual possibility of an oscillatory marginal regime. 

Notation cp = volume fraction, = correlation length, p= C./6, v= excluded volume parameter, 1 - 2x, N= number of bonds per chain, x= Flory-Huggins polymer-solvent interaction parameter, Vc = cross-over from swollen to ideal. Subscripts cr = critical, / = ideal, d = dilute, s = semi-dilute, m = marginal regime, c = concentrated regime, ov= cross-over from dilute to semi-dilute, cp = cross-over from concentrated to phase separated, sm = cross-over from semi-dilute to marginal, me = cross-over from marginal to concentrated. 

Structural analysis of the solid rocket case-grain system using experimentally determined propellant response properties may permit a complete description of the combined stresses and resultant deformations, but a statement expressing the ability of the propellant to withstand these stresses is also required. Such a statement, which relates the physical state at which failure occurs to some material parameters, is called a failure criterion. The criterion for failure permits a prediction of safety margins expected under motor operation and handling and defines the loading regimes where abnormal operations will occur with intolerable frequency. 

As tariffs in the secondary market are market clearing, the owners also collect the full scarcity payments. Hence, the investment incentives should be better than under a marginal cost-pricing regime. The owners rights are pursued, as they are given priority when capacity is scarce, nor are they being inadequately compensated by low tariffs. 

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