The Critical Instability Limit

Similarly, from the case i = 2 of (11.106a), we obtain analogous stability constraints on the isothermal compressibility fiT  

If we consider the general volume dependence of f3T in the limits of large or small V, we can see that (11.110) requires, in the small-V limit, 

If we consider the 2 x 2 determinantal constraint (11.106b), we can similarly infer the inequality 

Many similar asymptotic restrictions can be obtained from other matrix elements of M or M in standard or transformed coordinates. 

In many respects, the most dramatic, beautiful, and profound feature of a thermodynamic system is associated with the critical instability limit 

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Third, since the pulsating instability observed for the planar unstretched flame was expected to be promoted by positive stretch, pulsation may develop beyond a critical stretch rate smaller than the static extinction limit. As pulsating extinction occurred at a smaller stretch rate than the steady extinction limit, the flame extinguished in the pulsating, instead of the steadily propagating mode, and the flammable range was accordingly narrowed. 

Later, the critical Re was further raised for pipe flows, establishing that there is perhaps no upper limit above which transition to turbulence can not be prevented. This example also suggests the importance of receptivity of flow to different types of input disturbances to the system. If there is no input to a fluid dynamical system of a particular kind that triggers instability, then the response will demonstrate the flow to be orderly, even if the fluid dynamical system is unstable to that kind of input. Thus, if the basic flow is receptive to a particular disturbance, then the equilibrium flow will not be observable in the presence of such disturbances. 

It follows that the evaluation of the extent to which one-dimensional physics is relevant has always played an important part in the debate surrounding the theoretical description of the normal state of these materials. One point of view expressed is that the amplitude of in the b direction is large enough for a FL component to develop in the ab plane, thereby governing most properties of the normal phase attainable below say room temperature. In this scenario, the anisotropic Fermi liquid then constitutes the basic electronic state from which various instabilities of the metallic state, like spin-density-wave, superconductivity, etc., arise [29]. Following the example of the BCS theory of superconductivity in conventional superconductors, it is the critical domain of the transition that ultimately limits the validity of the Fermi liquid picture in the low temperature domain. 

P = effective permeability, r = intestinal radius, and = residence time in the small intestine [2]. The critical assumptions in this relationship are (1) that the drug is in solution and hence available for transport across the intestinal membrane and (2) the drug is chemically stable in the gastrointestinal tract and not a substrate for proteolytic or metabolic enzymes in the intestinal lumen or gut mucosa. These are highly simplifying assumptions. The inappropriate use of Eq. (2) to calculate absorption for compounds that are limited by solubility, instability, or metabolism can lead to seriously erroneous and misleading conclusions. 

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