Thin-source concentration dependent diffusion volume II
Abstract
I. PreliminariesAt the end of Chapter 6, Sec.V , the grand minimizing functional for the non-linear equation, capable of handling a multiple time correlation, was presented.Denoting a set of 'N' measured profiles by: (Sl)' (S2), (S3), . .(S*N) a "two-time" correlation examining the propagation (S[Initial])+(S[Final]) 2 2 involves 1-term in the (D -function.Thus, 'NK' terms in (D is an "NK+1"time correlation, composed of subunit 2-time correlations.Given 'N' 1' .. measured profiles, many different correlations are possible.Some examples o f "3-time" correlations would be: Sequential: (Sl)+(S2); (S2)+(S3) Sl+S2+S3Alternating:(the last column.beinga shortened notation).Clearly for even 4 or 5 measured profiles, the totality of correlations, each of which is a separate non-linear .analysis, is quite large.Thus, in this work, we will concentrate on the 'sequential' correlations, which should show how the non-linear effects change as the concentration decreases, and the 'pinned' correlations which show how easily a given final state is reached from various (different time) "initial" states._* Each subunit 2-time correlation uses an initial state [C(x,r :k )] which is propagated forward to give a state [C(x,r(k );k )] which can then .*Wbe compared to a measured final state [C(x,I' ;k )].As outlined in Chapter 6, the propagated state: C(x,r(kj);kj) = 00(x) + 001(x) + a202(x) + 803(x) (8.01) can be derived in accordance with 6 independent models; each model being a distinct…
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