Conservation equation, renormalization

According to Eq. (5.52), the function f t g,fo) is an invariant of a renormalization procedure, in the course of which the generalized time is divided into tjx steps, each of length, x, the bare coupHng parameter is replaced by its effective counterpart and the initial value of the function at t = 1 is replaced with the function evaluated at the new scale length x. In the limit g( = 0 the conservation equation (5.52) must reduce to the corresponding equation (5.6), appropriate to the ideal system. Therefore, the effective coupling function must satisfy the condition g t 0) = 0, Vt. 

Although the equation of evolution for g(t g) now has been identified, we still must specify the relationship between this function and the object function f t,g,f. We also must develop a practical, computational procedure for implementing the multiplicative RG method. These items will be treated in the following sections. However, before proceeding to these issues it is worthy of notice that in standard formulations of the theory the equations of evolution are derived not from the conservation equation (5.52), as given above, but by postulating a proportionality between the original and renormalized excess functions. This postulate can be written in the form... 

Besides these stochastic interpretations, deterministic interpretations are presently developed GRAY [12], KUMPINSKY and EPSTEIN [13], propose systemic approaches, commonly used in chemical engineering several ideal reactors are coupled by conservative flows with expandable coefficients, so that by-passes or dead zones may be taken into account. NICOLIS and FRISCH 14] use a quasi-Semenov equation in the limit of large diffusion coefficients and obtain a renormalization of k , DEWEL et al. [15] use a phenomenological theory of turbulent mixing to study surface effects produced by the feed of the reactor. 

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