Unperturbed configuration average

Curtiss et al. (102a) have recently developed general formulas for t]0 — t]s and Je° for free-draining bead-connector models with arbitrary numbers of beads, connecting arrangements and force-distance laws for the connectors. The expressions depend on averages over the unperturbed distribution of configurations for the model ... 

The Mjy and My emissions give the position of the 5/ distributions, whatever the characteristics of these states—if they are localized, the hole is filled very rapidly by an Auger-type process — if not, the mobility of the hole is large thus, at the final state of the process, the average configuration on each atom has a strong probability of being that of unperturbed metals as this is always the case for the emission band of metals. 

Let us note, that there are two classes of problems, dealing with disorder, utunely those with annealed and quenched disorder. In the first case, the different realizations of disorder are averaged simultaneously with a thermodynamical averaging over different conformations of the SAW. In the present review, we however focus on the case of quenched disorder [15], which is introduced such that it is not in thermodynamic equilibrium with the unperturbed system. The quantities of physical interest must then first be calculated for a particular configuration of disorder, followed by the average over all configurations of disorder. 

Chemical potential profile, p(z), of solute across a hpid bilayer and adjacent water phase is obtained by inserting the solute numerous times into randomly selected positions in the system obtained by MD simulation and calculating the interaction energy, E(z), between the inserted solute and all the molecules in the system. From t, where <...>t denotes the thermal average over insertions of solute with randomly chosen orientations into configurations of the system at depth z unperturbed by the solute, the excess chemical potential, p(z), and thereby the free energy of transfer, AG(z), from bulk water to the bilayer interior at the depth z are obtained AG(z) =p (z) - ]i (water)... 

We require also the possibility P(ii) of a set of configurations having the average density corresponding to the dilation relative to the probability of a set of configurations for which the density of segments corresponds to = 1. For the former, the mean-squared separation of the ends of the chain is for the latter it is . The distribution of chain vectors r for the unperturbed chain is approximately Gaussian as noted above. 

---