Irreversible survival probability

Figure 1.4 Irreversible survival probability p[t) = (0 V (t)>p as a function of time. Recurrences occur at times tj. = Inkh/S k = 1,2.(<5 = 1, arbitrary units).

For large negative AG, the transfer becomes irreversible Wb < W. Setting Wb = 0 and W = W(r), we obtain under this condition a single equation for the survival probability of the initially excited state ... 

Figure 9.14. Survival probability S(t) of an irreversible ET reaction [Pi(t) in our notation] in the solvent-controlled regime (k -> co) for biexponential solvent relaxation model with the normalized correlation function A(t) The parameter AG is the activation... 

Figure 9.23. Survival probability S(t) of an irreversible activationless ET reaction [P,(t) in our notation] in the solvent-controlled regime (k -> oo) obtained by Monte Carlo sampling for the Gaussian-correlated process ( ) and the two-component process with C(t)/C(0) = 0.8 tp[ —(t/Tj) ] -H 0.2exp[ —t/(10Tj)] (A) and C(0) = 16 in both cases. Time is in units of t,. Inset the same data replotted on a semilog scale. (Reproduced from [120b] with permission. Copyright (1995) by Elsevier Science.)...

Another peculiarity of the study is that the use of a biological system has allowed the authors to hypothesize a possible mechanism of action of the leachate as a mixture, hypothesis that could have been drafted on the basis of the only knowledge derived by chemical analysis. Researchers suggest that leachate inhibits cell proliferation at low doses probably inducing a reversible cell cycle arrest that becomes irreversible at high doses, probably due to leachate-induced oxidative stress. This activity is mainly due to the chemical compounds extracted in the aqueous phase. Similar effects were noticed by previous investigations on other human cells (human peripheral blood lymphocytes and a human breast cancer cell line, MCF-7) [31, 32], supporting the hypothesis that cells that survive the initial insult from leachate constituents maintains the potential to proliferate until the effects on cell metabolism lead to death. 

Consider the irreversible two-compartment model with survival, distribution, and density functions starting time, the molecules are present only in the first compartment. The state probability p (t) that a molecule is in compartment 1 at time t is state probability p2 (/,) that a molecule survives in compartment 2 after time t depends on the length of the time interval a between entry and the 1 to 2 transition, and the interval I, a between this event and departure from the system. To evaluate this probability, consider the partition 0 = ai < a.2 < < o.n 1 < an = t and the n — 1 mutually exclusive events that the molecule leaves the compartment 1 between the time instants a, i and a,. By applying the total probability theorem (cf. Appendix D), p2 (t) is expressed as... 

P = probability for fatigue life survival Pirr = irreversible deformation power per unit of volume Q = heat flux Rk = Kapitza resistance S = cross-link distance or compliance tensor T = temperature U = internal energy Us = stored stress energy... 

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