Time-Dependent Restraints

A. E. Torda, R. M. Scheek, and W. F. van Gunsteren, Chem. Phys. Lett., 157, 289 (1989). Time-Dependent Distance Restraints in Molecular Dynamics Simulations. 

Of these three conditions derived by Pontryagin to treat the problem of state restraints, the most significant is that of Eq. (52), the time dependence of the additional Lagrange multiplier. The use of this condition is illustrated in the following section in the context of the xenon shutdown problem. 

Permeability is so low that, in sorption experiments, large pressure differences and membranes of small thickness have to be employed. These restraints do not apply to condensable vapours or highly permeant gas. In the last case, relaxation processes in the polymer matrix cause changes in the transport behaviour and make the permeability time-dependent. In contrast, only vapours of sufficiently high solubiUty are suitable for the gravimetric measurements used in the sorption experiments. Consequently, there are only few systems for which both sorption and permeation results have been reported. Low et al. conducted the two types of moisture transport experiments on a polyamide 6/elay nanocomposite. The authors found that the activation energy of moisture permeation obtained from the sorption experiment is lower than that derived from the permeation measurement. They concluded that the interaction and contribution of the diffusion and solubility parameters show complex transport behaviour in these nanocomposite films. 

Secondly, selectivity is not always achievable. For example, permselectivity of ion-exchanging polymer films fails at high electrolyte concentration. We have shown that even if permselectivity is not thermodynamically found, measurements on appropriate time scales in transient experiments can lead to kinetic permselectivity. To rationalise this behaviour we recall that the thermodynamic restraint, electrochemical potential, can be split into two components the electrical and chemical terms. These conditions may be satisfied on different time scales. Dependent on the relative transfer rates of ions and net neutral species, transient responses may be under electroneutrality or activity control. 

When Europeans first arrived in North America, they encountered indigenous people who viewed nature as a community to which humans and all other living things belonged and upon which all humans depended. The native people modified the environment with fire and took from it the plants and animals they needed, but with considerable restraint. We now know that in prehistoric times, large mammals had been driven to extinction at least partly by human agency, but for the most part the indigenous people of North America lived within nature s limits. 

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